Solve the given equation x2 - 4x - 2 = 0 and express your answer correct to two places of decimal.
Given, equation : x2 - 4x - 2 = 0.
By formula,
x = −b±b2−4ac2a\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}2a−b±b2−4ac
Substituting values we get :
⇒x=−(−4)±(−4)2−4×1×−22×1=4±16+82=4±242=4±262=2±6=2+6,2−6=2+2.449,2−2.449=4.449,−0.449\Rightarrow x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4 \times 1\times -2}}{2 \times 1} \\[1em] = \dfrac{4 \pm \sqrt{16 + 8}}{2} \\[1em] = \dfrac{4 \pm \sqrt{24}}{2} \\[1em] = \dfrac{4 \pm 2\sqrt{6}}{2} \\[1em] = 2 \pm \sqrt{6} \\[1em] = 2 + \sqrt{6}, 2 - \sqrt{6} \\[1em] = 2 + 2.449, 2 - 2.449 \\[1em] = 4.449, -0.449⇒x=2×1−(−4)±(−4)2−4×1×−2=24±16+8=24±24=24±26=2±6=2+6,2−6=2+2.449,2−2.449=4.449,−0.449
Hence, x = 4.449 or -0.449
